Certificate for #3787 ⟨a, b | ababbbaaab=a⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
• Auxiliary generators:
  1. abbb=c

Axiom: ababbbaaab=a.

Referenced by [3].

Axiom: abbb=c.

Referenced by [3], [4], [6].

Overlap of [1] ababbbaaab=a with [2] abbb=c:

Critical pair: abcaaab=a.

Referenced by [4], [5], [7], [8], [9], [10].

Overlap of [3] abcaaab=a with [2] abbb=c:

Critical pair: abcaac=abb.

Flip LHS and RHS.

Referenced by [6], [8], [11].

Overlap of [3] abcaaab=a with [3] abcaaab=a:

Critical pair: abcaaa=acaaab.

Referenced by [8], [9], [12].

Overlap of [2] abbb=c with [4] abb=abcaac:

Critical pair: abcaacb=c.

Referenced by [7], [13].

Overlap of [3] abcaaab=a with [6] abcaacb=c:

Critical pair: abcaac=acaacb.

Referenced by [8], [9].

Overlap of [3] abcaaab=a with [5] abcaaa=acaaab:

Critical pair: acaaabb=a.

Reduce LHS:

Referenced by [9].

Overlap of [3] abcaaab=a with [7] abcaac=acaacb:

Critical pair: abcaaacaacb=acaac.

Reduce LHS:

Defines rule #5.

Referenced by [10], [11], [12], [13].

Overlap of [3] abcaaab=a with [9] ab=acaac:

Critical pair: acaaccaaab=a.

Reduce LHS:

Defines rule #4.

Referenced by [14], [15], [16], [17].

Overlap of [4] abb=abcaac with [9] ab=acaac:

Critical pair: acaacb=abcaac.

Reduce RHS:

Defines rule #7.

Referenced by [16].

Overlap of [5] abcaaa=acaaab with [9] ab=acaac:

Critical pair: acaaccaaa=acaaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [17].

Overlap of [6] abcaacb=c with [9] ab=acaac:

Critical pair: acaaccaacb=c.

Defines rule #9.

Referenced by [15].

Overlap of [10] acaaccaaacaac=a with [10] acaaccaaacaac=a:

Critical pair: acaaccaaacaa=aaaccaaacaac.

Flip LHS and RHS.

Defines rule #3.

Overlap of [10] acaaccaaacaac=a with [13] acaaccaacb=c:

Critical pair: acaaccaaacac=aaaccaacb.

Flip LHS and RHS.

Defines rule #8.

Overlap of [10] acaaccaaacaac=a with [11] acaacb=acaaccaac:

Critical pair: acaaccaaacaacaaccaac=aaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [10] acaaccaaacaac=a with [12] acaaacaac=acaaccaaa:

Critical pair: acaaccaaacaacaaccaaa=aaaacaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.